In the early days of New Labour it is said a media adviser whispered into an ambitious minister's ear after an interview: "We don't say equality, we say fairness." The former reeked of socialism – all taxes, empowerment schemes and regulation. The latter was as inoffensive as a scented candle. Everyone can agree to be fair – which is the problem.

A fairness boom is under way. Two parties used the word in their election slogans. In their conference speeches Nick Clegg, Ed Miliband and David Cameron all promised to pursue fairness. In his new book Will Hutton argues we should do the same. Tomorrow the Equalities and Human Rights Commission (EHRC) publishes a 700-page report entitled How Fair Is Britain?, which turns out to be only partly about fairness – in the sense of discrimination – but about inequalities of outcome too.

John Rawls, whose defence of fairness as a form of justice must have hung over the student PPE essays of both the prime minister and the leader of the opposition, saw the importance of fair opportunity in a liberal society, and understood that would not produce equal outcomes. But diluted by politics, fairness has become as milky as the word progressive, degraded into irrelevance by overuse.

Politicians like fairness because it cannot be measured. It compels no action; it is an atmospheric ideal, an invisible gas, a miasma. It is, in Churchill's expression, a "happy thought". We might as well promise to be nice, or a bit understanding, or champion the merits of compassion, or just cuddle each other.

More honestly, we could skip the miasma altogether and confess to wanting a mildly unjust, economically unequal but often successful society in which we are spared extremes. This does not sound a bad prospect: but we should not deny that it may produce outcomes describable as unfair.

The point, as every parent tells their child, is that life isn't fair. Not everything can or will be the same. Life is an erratic blend of luck, ability and effort. We should encourage effort and hope for ability, and try to minimise dependence on luck. But we are fooling ourselves if we think we can eradicate inequality.

The EHRC report is full of dismaying facts about social dysfunction – and is to be welcomed for identifying them. One in four Welsh adults are illiterate. One in two people in England and Wales are largely innumerate. The average wealth of the poorest 10% in society is 100 times less than that of the richest 10%.

No citizen should be content with this. But the report does not ask whether there is a fair level of inequality we should find tolerable. Its definition of a fair society is one that champions the constant reduction of unequal outcomes.

I think the EHRC has a wrongheaded idea of fairness. It measures the extent to which people's lives are different, and then calculates the action needed to make them more the same. The assumption is that equality is what we all want.

This overlooks the possibility that the actions needed to compel equality may be seen as unfair by those who do not benefit from them. An equally valid idea of a fair society may be one in which people are given the space and the right to strive for inequality: advantage achieved by their own efforts.

This sounds horribly right wing. But there is a challenge for the right in this too. The corollary of rejecting equality as a goal, and placing greater responsibility on individuals, must be to increase opportunity by reducing unfair advantage. If the state is to do less to bail people out of disasters of their own making, it must do more to give people a chance to avoid disaster in the first place.

We are very bad at that in Britain. As the report says, inequality of income is less sharp than inequality of wealth. People inherit privilege. They buy their way into private schools. Others get trapped in generational cycles, as Iain Duncan Smith is not the first to point out. State mechanisms for releasing them have not worked despite a decade of never-to-be-repeated support. To the extent that Labour reduced poverty at all, it was by shoving large sums of cash from the rich – and the budget deficit – to the poor. This didn't make the country fairer: it simply papered over the underlying unfairness.

If we are not to discard fairness as a useless concept, we must sharpen its definition. A liberal government like the one we have now cannot be content with reducing benefits for all and hoping people will call that fair. That's fairness as a flabby excuse for cuts. It is right that people on high incomes should not have benefits protected when those lower down do not, but deeper fairness demands giving people the chance to make something of their lives and not be held down by inherited disadvantages.

The tough choice for the left is to understand the impossibility and undesirability of equality. The tough choice for the right is to realise that a divided and hierarchical society cannot – in the best sense of that word – be fair.